D.4 Trap-Assisted Tunneling

If the keyword tat is set in the TsuEsaki tunneling model, an additional trap-assisted tunneling current is calculated. The oxideTrap model must be used to specify the trap properties. Input deck parameters of this model are the electron mass in the dielectric, the emitted phonon energy $\hbar \omega$, and the Huang-Rhys factor $S$ which can be used as a fitting parameter. The following code shows an example input deck. The model keywords are listed in Table D.4.

  Phys 
  { 
     tunnel = addNearestInterfaces("Device", "GateOxide");
     +GateOxide
     {
        oxideTrap = "Pure";
        OxideTrap
        {
           Pure
           {
              Nt        = 1e19 "cm^-3"; // trap concentration
              type      = "negative";   // charge state
              occupancy = 0.0;          // trap occupancy
              energy    = 3 "eV";       // trap energy level
           }
        }
        Electron
        {
           tunnel = "TsuEsaki";
           Tunnel
           {
              TsuEsaki
              {
                 direct     = no;        // consider direct tunneling
                 tat        = yes;       // consider trap-assisted tunneling
                 mOx        = 0.5;       // electron mass in the dielectric 
                 consistent = yes;       // self-consistency 
                 tcType     = "qtbm";    // "analyticalWKB,qtbm"
                 dfType     = "fermi";   // "general"
                 dNrg       = 10 "meV";  // energy step for integration
                 huangRhys  = 65;        // for trap-assisted tunneling
                 phononNrg  = 0.03 "eV"; // for trap-assisted tunneling 
                 imageForce = no;        // image force correction
              }
           }
         }
     }
  }

A. Gehring: Simulation of Tunneling in Semiconductor Devices